The purpose of this model is to understand how genetic architectures of alternative reproductive tactics impact their maintenance in populations. I’m using an individual-based simulation model with different selection scenarios, types of alternative tactics, and genetic architectures (genome-wide additive genetic variance, supergenes, expression networks).

Overview of the model

Males can be courters or not-courters and parents or not-parents. When the model is run with both traits, this results in four possible morphs: courter/parent, courter/not-parent, not-courter/parent, and not-courter/not-parent. Generations are non-overlapping and there is one reproductive bout per generation. In each generation, the population follows the following timeline:

1. Choosing a nest

A female samples 50 males and chooses a male to nest with based on his courtship trait. If there are no courtship traits in the model, she chooses based on the male’s parental trait. If she does not encouter an acceptable male, she does not nest. If she encounters multiple equally-acceptable males, she randomly selects one of them.

2. Fertilization

Once a female decides to nest, up to three males can fertilize the nest. Courters and parental males can contribute more sperm than non-courter and non-parental males: \(r_{courter}=r_{parent}=8\) and \(r_{non-courter}=r_{non-parent}=4\). A courter/non-parent has \(r_{non-parent}\) and a non-courter/parent has \(r_{parent}\). The male with whom the female is nesting gets \(r_{parent}/\Sigma{n_{sperm}}\) and additional non-parental males (up to 2) get \((r_{non-parent}*0.5/\Sigma{n_{sperm}})\), where \(\Sigma{n_{sperm}}\) is the total number of sperm contributed by all of the males, weighted by the sperm competition factor (0.5 is the default for all males except the nesting male). So, when a female mates with one courter and two non-parentals, \(\Sigma{n_{sperm}}\) = \(r_{courter}\) + 2\(*\)(0.5\(*\)\(r_{sneaker}\)), where \(r_{courter}\) = 8 and \(r_{sneaker}\) = 4, therefore \(\Sigma{n_{sperm}}\) = 12.

That being said, every time a male mates he uses his sperm, so after one mating where a courter fertilizes 50% of the female’s 4 eggs, he only has 6 sperm for his next mating.

3. Nest Survival

Before the babies can survive, the nest has to survive. This step is only relevant when parental traits are in the model - if only the courtship trait is specified, then all progeny in the nest survive at this point. When males have the parental trait, if the female has given eggs to a non-parental male (because she chose based on courtship traits), then the nest has a 10% chance of surviving. If the female has given eggs to a parental male, the nest has a 90% chance of surviving.

4. Density-dependent survival

Once the identities of the surviving nests are known–along with the identities of the parents, including sneaker parents–the offspring are created in the simulation. The offspring are created to fill the full carrying capacity of the population, with the numbers per nest being equally divided among all surviving offspring. This allows the population to maintain a constant population size (prior to viability selection) while maintaining the relative successes of the given genotypes/morphs.

5. Viability selection

Before becoming adults, the offspring experience viability selection. Courters and parental males are disfavored in viability selection, with a survival probability of 0.9950125. If an individual is both a courter and a parental male, the survival probability is 0.9900498. Non-courters and non-parental males have survival probabilities of 1.

Evaluating equilibrium

After 10000 generations, I begin tracking the change in frequency of the courter and parent traits, and do so for 2000 additional generations. I calculate the variance in the change in frequency over those 2000 generations. I declare an equilibrium (‘stasis’) has been reached if the last change in frequency of both traits is less than the variance in changes in frequency.

Unlinked additive genetic variance

In these cases, the traits are encoded by a number (50) of loci, whose alleles contribute additively to determine the trait value. These alleles are all freely recombining and are not adhered to any physical genomic location (aka this is a classical quantitative genetics approach). The overall trait value is compared to a population-level threshold (which is static, in these cases), and if the trait value is above the threshold the male takes the parent or courter morph and if it is below he does not. Below, I’m showing the results from 10 replicates of each scenario.

Courter trait

Females choose nests based on whether the male is a courter or not, and they all prefer courters all of the time (the female preference does not have a genetic basis and does not evolve). The only way that non-courters produce offspring is through sneaking, but all males can be sneakers (both courters and non-courters). Because parental care is not incorporated in this model, all nests survive.

Frequency of the courter morph (each color represents a different replicate)

Frequency of the courter morph (each color represents a different replicate)

Of the 20 replicates, 0 reached an equilibrium by 10000 generations.

Frequency of courters in final generation
CourterFreq CourterW NonCourterW
courter_unlinked_1_summary.txt_1 1 2.05590 0
courter_unlinked_1_summary.txt_2 1 2.01417 0
courter_unlinked_1_summary.txt_3 1 1.94737 0
courter_unlinked_1_summary.txt_4 1 1.95088 0
courter_unlinked_2_summary.txt_1 1 2.07500 0
courter_unlinked_2_summary.txt_2 1 2.01826 0
courter_unlinked_2_summary.txt_3 1 2.00402 0
courter_unlinked_2_summary.txt_4 1 1.95669 0
courter_unlinked_3_summary.txt_1 1 2.01623 0
courter_unlinked_3_summary.txt_2 1 2.17211 0
courter_unlinked_3_summary.txt_3 1 1.92100 0
courter_unlinked_3_summary.txt_4 1 2.08142 0
courter_unlinked_4_summary.txt_1 1 2.02236 0
courter_unlinked_4_summary.txt_2 1 2.08595 0
courter_unlinked_4_summary.txt_3 1 1.96647 0
courter_unlinked_4_summary.txt_4 1 2.08159 0
courter_unlinked_5_summary.txt_1 1 1.96443 0
courter_unlinked_5_summary.txt_2 1 1.97610 0
courter_unlinked_5_summary.txt_3 1 1.93023 0
courter_unlinked_5_summary.txt_4 1 2.04294 0

Parental trait

All females nest with parental males, so the only way non-parental males reproduce is through sneaking. Parental males provide care that allows nests to have a 90% chance of survival. The female preference does not have a genetic basis and does not evolve.

Frequency of parent morph (each color represents a different replicate)

Frequency of parent morph (each color represents a different replicate)

Frequency of parents in final generation
ParentFreq ParentW NonParentW
parent_unlinked_1_summary.txt_1 0.569288 1.38158 0.452174
parent_unlinked_1_summary.txt_2 0.562753 1.52878 0.268519
parent_unlinked_1_summary.txt_3 0.558935 1.34014 0.267241
parent_unlinked_1_summary.txt_4 0.540797 1.31579 0.181818
parent_unlinked_2_summary.txt_1 0.878486 1.58957 0.786885
parent_unlinked_2_summary.txt_2 0.913725 1.66953 1.090910
parent_unlinked_2_summary.txt_3 0.874747 1.68129 0.467742
parent_unlinked_2_summary.txt_4 0.847561 1.71942 0.560000
parent_unlinked_3_summary.txt_1 0.556936 1.59480 0.411215
parent_unlinked_3_summary.txt_2 0.521472 1.55686 0.423077
parent_unlinked_3_summary.txt_3 0.590164 1.55208 0.240000
parent_unlinked_3_summary.txt_4 0.607438 1.52721 0.368421
parent_unlinked_4_summary.txt_1 0.587771 1.53691 0.263158
parent_unlinked_4_summary.txt_2 0.581349 1.58703 0.436019
parent_unlinked_4_summary.txt_3 0.511905 1.37597 0.284553
parent_unlinked_4_summary.txt_4 0.594961 1.36156 0.334928
parent_unlinked_5_summary.txt_1 0.595057 1.45687 0.323944
parent_unlinked_5_summary.txt_2 0.518219 1.44922 0.386555
parent_unlinked_5_summary.txt_3 0.475410 1.46552 0.363281
parent_unlinked_5_summary.txt_4 0.584980 1.43243 0.290476

Variation was maintained in 20 of the 20. 0 of the 20 populations crashed, though. Of the 20 replicates, 20 reached an equilibrium by 10000 generations.

Courtship and Parental Traits

Females choose nests based on males’ courtship trait (they all only nest with courting males, and the female preference does not have a genetic basis and does not evolve), and then the survival of the nest depends on whether the courting male is also a parental male. If the chosen male is a parental male, the nest has a 90% chance of survival. Otherwise, it only has a 10% chance. Non-courters only reproduce through sneaking.

The different runs have different outcomes.

Let’s look at the morph frequencies.

Frequency of the 4 morphs in each rep

Frequency of the 4 morphs in each rep

In some of the runs the population crashed after few generations. This is obvious when looking at the the final frequencies in a table as well:

Frequency of morphs in final generation
Generation CourterThresh CourterFreq CourterW NonCourterW
parent-courter_unlinked_1_summary.txt_1 361 -0.3606110 0.566667 0.235294 0
parent-courter_unlinked_1_summary.txt_2 361 -0.3606110 1.000000 0.000000 0
parent-courter_unlinked_1_summary.txt_3 361 -0.3606110 0.729730 0.148148 0
parent-courter_unlinked_1_summary.txt_4 360 -0.3606110 1.000000 3.000000 0
parent-courter_unlinked_2_summary.txt_1 1170 -0.0016371 0.750000 0.904762 0
parent-courter_unlinked_2_summary.txt_2 150 -0.0016371 0.750000 0.000000 0
parent-courter_unlinked_2_summary.txt_3 1170 -0.0016371 0.916667 0.318182 0
parent-courter_unlinked_2_summary.txt_4 1169 -0.0016371 1.000000 1.500000 0
parent-courter_unlinked_3_summary.txt_1 348 -0.4853490 1.000000 0.000000 0
parent-courter_unlinked_3_summary.txt_2 815 -0.4853490 0.500000 4.000000 0
parent-courter_unlinked_3_summary.txt_3 815 -0.4853490 1.000000 0.000000 0
parent-courter_unlinked_3_summary.txt_4 815 -0.4853490 1.000000 0.666667 0
parent-courter_unlinked_4_summary.txt_1 572 -1.2749400 0.500000 0.319277 0
parent-courter_unlinked_4_summary.txt_2 572 -1.2749400 0.694444 0.280000 0
parent-courter_unlinked_4_summary.txt_3 366 -1.2749400 1.000000 0.000000 0
parent-courter_unlinked_4_summary.txt_4 571 -1.2749400 1.000000 4.000000 0
parent-courter_unlinked_5_summary.txt_1 11999 -0.1447760 0.559471 0.299213 0
parent-courter_unlinked_5_summary.txt_2 11999 -0.1447760 0.550661 0.377510 0
parent-courter_unlinked_5_summary.txt_3 11999 -0.1447760 0.564482 0.370787 0
parent-courter_unlinked_5_summary.txt_4 11999 -0.1447760 0.559072 0.524528 0

Multiple morphs are maintained in 20 of the 20 replicates, and those morphs contain either a parent or a courter. However, 16 of those reps with variation actually crashed.

Linked additive genetic variance

Courter trait

Frequency of the courter morph with linked QTLs (each color represents a different replicate)

Frequency of the courter morph with linked QTLs (each color represents a different replicate)

Of the 20 replicates, 0 reached an equilibrium by 10000 generations.

Frequency of courters with linked QTLs in final generation
CourterFreq CourterW NonCourterW
courter_linked_1_summary.txt_1 1 1.98020 0
courter_linked_1_summary.txt_2 1 2.10526 0
courter_linked_1_summary.txt_3 1 1.95695 0
courter_linked_1_summary.txt_4 1 2.07469 0
courter_linked_2_summary.txt_1 1 1.96640 0
courter_linked_2_summary.txt_2 1 2.03265 0
courter_linked_2_summary.txt_3 1 2.06198 0
courter_linked_2_summary.txt_4 1 1.96647 0
courter_linked_3_summary.txt_1 1 2.01613 0
courter_linked_3_summary.txt_2 1 1.98020 0
courter_linked_3_summary.txt_3 1 1.96464 0
courter_linked_3_summary.txt_4 1 1.95695 0
courter_linked_4_summary.txt_1 1 2.07724 0
courter_linked_4_summary.txt_2 1 2.00401 0
courter_linked_4_summary.txt_3 1 1.97610 0
courter_linked_4_summary.txt_4 1 2.08386 0
courter_linked_5_summary.txt_1 1 1.91154 0
courter_linked_5_summary.txt_2 1 1.92486 0
courter_linked_5_summary.txt_3 1 1.96260 0
courter_linked_5_summary.txt_4 1 1.99599 0

Every rep has the courtship trait go to fixation.

Parental trait

All females nest with parental males, so the only way non-parental males reproduce is through sneaking. Parental males provide care that allows nests to have a 90% chance of survival. The female preference does not have a genetic basis and does not evolve.

Frequency of parent morph with linked QTLs (each color represents a different replicate)

Frequency of parent morph with linked QTLs (each color represents a different replicate)

Frequency of parents with linked QTLs in final generation
ParentFreq ParentW NonParentW
parent_linked_1_summary.txt_1 0.833689 1.81841 0.705128
parent_linked_1_summary.txt_2 0.857143 1.59111 0.626667
parent_linked_1_summary.txt_3 0.801158 1.62651 0.533981
parent_linked_1_summary.txt_4 0.832990 1.67822 0.716049
parent_linked_2_summary.txt_1 0.802444 1.59391 0.587629
parent_linked_2_summary.txt_2 0.805447 1.58454 0.540000
parent_linked_2_summary.txt_3 0.795203 1.41995 0.369369
parent_linked_2_summary.txt_4 0.775194 1.54250 0.543103
parent_linked_3_summary.txt_1 0.901840 1.74603 0.625000
parent_linked_3_summary.txt_2 0.881497 1.75000 0.824561
parent_linked_3_summary.txt_3 0.866667 1.78125 0.921875
parent_linked_3_summary.txt_4 0.878486 1.75057 0.967213
parent_linked_4_summary.txt_1 0.820619 1.64824 0.655172
parent_linked_4_summary.txt_2 0.846774 1.64524 0.763158
parent_linked_4_summary.txt_3 0.834343 1.69249 0.451220
parent_linked_4_summary.txt_4 0.846743 1.58371 0.375000
parent_linked_5_summary.txt_1 0.839757 1.67874 0.405063
parent_linked_5_summary.txt_2 0.817822 1.64407 0.434783
parent_linked_5_summary.txt_3 0.810811 1.57619 0.357143
parent_linked_5_summary.txt_4 0.823748 1.66892 0.663158

Variation was maintained in 20 of the 20. 0 of the 20 populations crashed, though. Of the 20 replicates, 20 reached an equilibrium by 10000 generations.

Courtship and Parental Traits

Females choose nests based on males’ courtship trait (they all only nest with courting males, and the female preference does not have a genetic basis and does not evolve), and then the survival of the nest depends on whether the courting male is also a parental male. If the chosen male is a parental male, the nest has a 90% chance of survival. Otherwise, it only has a 10% chance. Non-courters only reproduce through sneaking.

Frequency of the two morphs with linked QTLs (courter = green, parent = blue)

Frequency of the two morphs with linked QTLs (courter = green, parent = blue)

The different runs have different outcomes.

Let’s look at the morph frequencies.

Frequency of the 4 morphs in each rep with linked QTLs

Frequency of the 4 morphs in each rep with linked QTLs

In some of the runs the population crashed after few generations. This is obvious when looking at the the final frequencies in a table as well:

Frequency of morphs in final generation (linked loci)
Generation CourterThresh CourterFreq CourterW NonCourterW
parent-courter_linked_1_summary.txt_1 11999 0.205997 0.570577 0.296167 0.0000000
parent-courter_linked_1_summary.txt_2 11999 0.205997 0.575397 0.393103 0.0000000
parent-courter_linked_1_summary.txt_3 11999 0.205997 0.578431 0.372881 0.0000000
parent-courter_linked_1_summary.txt_4 11999 0.205997 0.574468 0.363636 0.0000000
parent-courter_linked_2_summary.txt_1 11999 0.453996 0.586433 0.384328 0.0000000
parent-courter_linked_2_summary.txt_2 11999 0.453996 0.625000 0.380000 0.0000000
parent-courter_linked_2_summary.txt_3 11999 0.453996 0.581609 0.545455 0.0000000
parent-courter_linked_2_summary.txt_4 11999 0.453996 0.610778 0.254902 0.0153846
parent-courter_linked_3_summary.txt_1 11999 -0.248380 0.898000 1.870820 0.9803920
parent-courter_linked_3_summary.txt_2 11999 -0.248380 0.918580 1.847730 1.1794900
parent-courter_linked_3_summary.txt_3 11999 -0.248380 0.901031 1.823800 1.0833300
parent-courter_linked_3_summary.txt_4 11999 -0.248380 0.878558 1.753780 1.0781200
parent-courter_linked_4_summary.txt_1 11999 -0.851940 0.570039 0.532423 0.0000000
parent-courter_linked_4_summary.txt_2 11999 -0.851940 0.576471 0.445578 0.0000000
parent-courter_linked_4_summary.txt_3 11999 -0.851940 0.596078 0.322368 0.0000000
parent-courter_linked_4_summary.txt_4 11999 -0.851940 0.573413 0.429066 0.0000000
parent-courter_linked_5_summary.txt_1 11999 1.818740 0.898969 1.827980 0.8979590
parent-courter_linked_5_summary.txt_2 11999 1.818740 0.896907 1.878160 0.9400000
parent-courter_linked_5_summary.txt_3 11999 1.818740 0.911392 1.967590 1.1666700
parent-courter_linked_5_summary.txt_4 11999 1.818740 0.901852 1.636550 0.7924530

Multiple morphs are maintained in 20 of the 20 replicates, and those morphs contain either a parent or a courter. However, 0 of those reps with variation actually crashed.

Supergenes

Courter trait

Frequency of the courter morph with supergenes (each color represents a different replicate)

Frequency of the courter morph with supergenes (each color represents a different replicate)

Of the 20 replicates, 0 reached an equilibrium by 10000 generations.

Frequency of courters with supergenes in final generation
CourterFreq CourterW NonCourterW
courter_supergene_1_summary.txt_1 1 2.03901 0
courter_supergene_1_summary.txt_2 1 2.12473 0
courter_supergene_1_summary.txt_3 1 2.06639 0
courter_supergene_1_summary.txt_4 1 1.89905 0
courter_supergene_2_summary.txt_1 1 2.04312 0
courter_supergene_2_summary.txt_2 1 1.96267 0
courter_supergene_2_summary.txt_3 1 2.05350 0
courter_supergene_2_summary.txt_4 1 2.09244 0
courter_supergene_3_summary.txt_1 1 2.00606 0
courter_supergene_3_summary.txt_2 1 1.89714 0
courter_supergene_3_summary.txt_3 1 1.90095 0
courter_supergene_3_summary.txt_4 1 2.03061 0
courter_supergene_4_summary.txt_1 1 2.02840 0
courter_supergene_4_summary.txt_2 1 2.04918 0
courter_supergene_4_summary.txt_3 1 1.98807 0
courter_supergene_4_summary.txt_4 1 2.01613 0
courter_supergene_5_summary.txt_1 1 2.05165 0
courter_supergene_5_summary.txt_2 1 2.05579 0
courter_supergene_5_summary.txt_3 1 2.03462 0
courter_supergene_5_summary.txt_4 1 2.00403 0

Parental trait

All females nest with parental males, so the only way non-parental males reproduce is through sneaking. Parental males provide care that allows nests to have a 90% chance of survival. The female preference does not have a genetic basis and does not evolve.

Frequency of parent morph with supergenes (each color represents a different replicate)

Frequency of parent morph with supergenes (each color represents a different replicate)

Frequency of parents with supergenes in final generation
ParentFreq ParentW NonParentW
parent_supergene_1_summary.txt_1 0.856833 1.71139 0.727273
parent_supergene_1_summary.txt_2 0.889780 1.62838 0.763636
parent_supergene_1_summary.txt_3 0.898635 1.59870 0.692308
parent_supergene_1_summary.txt_4 0.880567 1.68506 0.796610
parent_supergene_2_summary.txt_1 0.524950 1.49049 0.361345
parent_supergene_2_summary.txt_2 0.519270 1.48828 0.443038
parent_supergene_2_summary.txt_3 0.490982 1.51020 0.255906
parent_supergene_2_summary.txt_4 0.500000 1.40769 0.330769
parent_supergene_3_summary.txt_1 0.529897 1.33463 0.280702
parent_supergene_3_summary.txt_2 0.542169 1.48519 0.280702
parent_supergene_3_summary.txt_3 0.520000 1.38846 0.345833
parent_supergene_3_summary.txt_4 0.511811 1.44231 0.237903
parent_supergene_4_summary.txt_1 0.877510 1.66362 0.754098
parent_supergene_4_summary.txt_2 0.868526 1.64908 0.666667
parent_supergene_4_summary.txt_3 0.887029 1.73821 1.092590
parent_supergene_4_summary.txt_4 0.896907 1.71724 1.280000
parent_supergene_5_summary.txt_1 0.490196 1.44000 0.292308
parent_supergene_5_summary.txt_2 0.545639 1.37546 0.348214
parent_supergene_5_summary.txt_3 0.506173 1.68699 0.362500
parent_supergene_5_summary.txt_4 0.548000 1.44891 0.389381

Variation was maintained in 20 of the 20. 0 of the 20 populations crashed, though. Of the 20 replicates, 20 reached an equilibrium by 10000 generations.

Courtship and Parental Traits

Females choose nests based on males’ courtship trait (they all only nest with courting males, and the female preference does not have a genetic basis and does not evolve), and then the survival of the nest depends on whether the courting male is also a parental male. If the chosen male is a parental male, the nest has a 90% chance of survival. Otherwise, it only has a 10% chance. Non-courters only reproduce through sneaking.

Frequency of the two morphs with linked QTLs (courter = green, parent = blue)

Frequency of the two morphs with linked QTLs (courter = green, parent = blue)

The different runs have different outcomes.

Let’s look at the morph frequencies.

Frequency of the 4 morphs in each rep with supergenes

Frequency of the 4 morphs in each rep with supergenes

In some of the runs the population crashed after few generations. This is obvious when looking at the the final frequencies in a table as well:

Frequency of morphs in final generation (supergenes)
Generation CourterThresh CourterFreq CourterW NonCourterW
parent-courter_supergene_1_summary.txt_1 11999 -0.5236920 0.888158 1.987650 1.27451
parent-courter_supergene_1_summary.txt_2 11999 -0.5236920 0.950855 1.937080 2.47826
parent-courter_supergene_1_summary.txt_3 11999 -0.5236920 0.947808 1.768720 2.16000
parent-courter_supergene_1_summary.txt_4 11999 -0.5236920 0.929825 1.756810 1.36111
parent-courter_supergene_2_summary.txt_1 11999 0.0188334 0.897872 1.973930 1.16667
parent-courter_supergene_2_summary.txt_2 11999 0.0188334 0.916309 1.974240 1.89744
parent-courter_supergene_2_summary.txt_3 11999 0.0188334 0.882353 1.905750 1.05172
parent-courter_supergene_2_summary.txt_4 11999 0.0188334 0.904863 1.932240 1.48889
parent-courter_supergene_3_summary.txt_1 11999 0.7234720 0.578125 0.317568 0.00000
parent-courter_supergene_3_summary.txt_2 11999 0.7234720 0.583012 0.324503 0.00000
parent-courter_supergene_3_summary.txt_3 11999 0.7234720 0.578035 0.366667 0.00000
parent-courter_supergene_3_summary.txt_4 11999 0.7234720 0.582375 0.276316 0.00000
parent-courter_supergene_4_summary.txt_1 183 -0.4653770 1.000000 0.000000 0.00000
parent-courter_supergene_4_summary.txt_2 183 -0.4653770 0.622222 0.750000 0.00000
parent-courter_supergene_4_summary.txt_3 183 -0.4653770 0.514403 0.280000 0.00000
parent-courter_supergene_4_summary.txt_4 183 -0.4653770 0.588235 0.400000 0.00000
parent-courter_supergene_5_summary.txt_1 11999 1.1960700 0.917778 2.118640 1.37838
parent-courter_supergene_5_summary.txt_2 11999 1.1960700 0.934599 1.898420 1.41935
parent-courter_supergene_5_summary.txt_3 11999 1.1960700 0.911885 1.885390 1.44186
parent-courter_supergene_5_summary.txt_4 11999 1.1960700 0.934524 1.798300 1.48485

Multiple morphs are maintained in 20 of the 20 replicates, and those morphs contain either a parent or a courter. However, 4 of those reps with variation actually crashed.